Transport by meridional flows has significant consequences for stellar evolution, but is difficult to capture in global-scale numerical simulations because of the wide range of timescales involved. Stellar evolution models therefore usually adopt parameterizations for such transport based on idealized laminar or mean-field models. Unfortunately, recent attempts to model this transport in global simulations have produced results that are not consistent with any of these idealized models. In an effort to explain the discrepancies between global simulations and idealized models, we here use three-dimensional local Cartesian simulations of compressible convection to study the efficiency of transport by meridional flows below a convection zone in several parameter regimes of relevance to the Sun and solar-type stars. In these local simulations we are able to establish the correct ordering of dynamical timescales, although the separation of the timescales remains unrealistic. We find that, even though the generation of internal waves by convective overshoot produces a high degree of time dependence in the meridional flow field, the mean flow has the qualitative behavior predicted by laminar, "balanced" models. In particular, we observe a progressive deepening, or "burrowing", of the mean circulation if the local Eddington-Sweet timescale is shorter than the viscous diffusion timescale. Such burrowing is a robust prediction of laminar models in this parameter regime, but has never been observed in any previous numerical simulation. We argue that previous simulations therefore underestimate the transport by meridional flows.

Despite the success of the combination of conservative schemes and staggered constrained transport algorithms in the last fifteen years, the accurate description of highly magnetized, relativistic flows with strong shocks represents still a challenge in numerical RMHD. The present paper focusses in the accuracy and robustness of several correction algorithms for the conserved variables, which has become a crucial ingredient in the numerical simulation of problems where the magnetic pressure dominates over the thermal pressure by more than two orders of magnitude. Two versions of non-relativistic and fully relativistic corrections have been tested and compared using a magnetized cylindrical explosion with high magnetization ($ \ge 10^4$) as test. In the non-relativistic corrections, the total energy is corrected for the difference in the classical magnetic energy term between the average of the staggered fields and the conservative ones, before (CA1) and after (CA1′) recovering the primitive variables. These corrections are unable to pass the test at any numerical resolution. The two relativistic approaches (CA2 and CA2′), correcting also the magnetic terms depending on the flow speed in both the momentum and the total energy, reveal as much more robust. These algorithms pass the test succesfully and with very small deviations of the energy conservation ($\le 10^{-4}$), and very low values of the total momentum ($\le 10^{-8}$). In particular, the algorithm CA2′ (that corrects the conserved variables after recovering the primitive variables) passes the test at all resolutions. The numerical code used to run all the test cases is briefly described.

In this paper, we present the time evolution of a rotationally axisymmetric gas ring around a non rotating black hole using two dimensional grid-based hydrodynamic simulation. We show the way in which angular momentum transport is included in simulations of non-self-gravitating accretion of matter towards a black hole. We use the Shakura-Sunyaev {\alpha} viscosity prescription to estimate the turbulent viscosity. We investigate how a gas ring which is initially assumed to rotate with Keplerian angular velocity is accreted on to a back hole and hence forms accretion disc in the presence of turbulent viscosity. Furthermore, we also show that increase of the {\alpha} coefficient increases the rate of advection of matter towards the black hole. The density profile we obtain is in good quantitative agreement with that obtained from the analytical results. The dynamics of resulting angular momentum depends strongly on {\alpha}.

Previous MHD simulations have shown that wind must exist in black hole hot accretion flows. In this paper, we continue our study by investigating the detailed properties of wind, such as mass flux and poloidal speed, and the mechanism of wind production. For this aim, we make use of a three dimensional GRMHD simulation of hot accretion flows around a Schwarzschild black hole. The simulation is designed so that the magnetic flux is not accumulated significantly around the black hole. To distinguish real wind from turbulent outflows, we track the trajectories of the virtual Largrangian particles from simulation data. We find two types of real outflows, i.e., a quasi-relativistic jet close to the axis and a sub-relativistic wind subtending a much larger solid angle. Most of the wind originates from the surface layer of the accretion flow. The poloidal wind speed almost remains constant once they are produced, but the flux-weighted wind speed roughly follows $v_{\rm p, wind}(r)\approx 0.25 v_k(r)$. The mass flux of jet is much lower but the speed is much higher, $v_{\rm p,jet}\sim (0.3-0.4) c$. Consequently, both the energy and momentum fluxes of the wind are much larger than those of the jet. We find that the wind is produced and accelerated primarily by the combination of centrifugal force and magnetic pressure gradient, while the jet is mainly accelerated by magnetic pressure gradient. Finally, we find that the wind production efficiency $\epsilon_{\rm wind}\equiv\dot{E}_{\rm wind}/\dot{M}_{\rm BH}c^2\sim 1/1000$, in good agreement with the value required from large-scale galaxy simulations with AGN feedback.

Numerical simulations that reproduce solar-like magnetic cycles can be used to generate long-term statistics. The variations in N-S hemispheric cycle synchronicity and amplitude produced in simulations has not been widely compared to observations. The observed limits on asymmetry show that hemispheric sunspot area production is no more than 20% asymmetric for cycles 12-23 and phase lags do not exceed 20% (2 yrs) of the total cycle period. Independent studies have found a long-term trend in phase values as one hemisphere leads the other for ~four cycles. Such persistence in phase is not indicative of a stochastic phenomenon. We compare the findings to results from a numerical simulation of solar convection recently produced with the EULAG-MHD model. This simulation spans 1600 yrs and generated 40 regular, sunspot-like cycles. While the simulated cycle length is too long and the toroidal bands remain at too high of latitudes, some solar-like aspects of hemispheric asymmetry are reproduced. The model reproduces the synchrony of polarity inversions and onset of cycle as the simulated phase lags do not exceed 20% of the cycle period. Simulated amplitude variations between the N and S hemispheres are larger than observed in the Sun. The simulations show one hemisphere persistently leads the other for several successive cycles, placing an upper bound on the efficiency of transequatorial magnetic coupling mechanisms. These include magnetic diffusion, cross-equatorial mixing within elongated convective rolls and transequatorial meridional flow cells. One or more of these processes may lead to magnetic flux cancellation whereby the oppositely directed fields come in close proximity and cancel each other across the magnetic equator late in the solar cycle. We discuss the discrepancies between model and observations and the constraints they pose on possible mechanisms of hemispheric coupling.

We use a collective coordinate approximation to model the scattering of two solitons in modified nonlinear Schr\"odinger and sine-Gordon systems. We find that the anomalies of the conservation laws of the charges as calculated using the collective coordinate approximation demonstrate the same dependence on the symmetry of the field configuration as that previously found analytically and using a full numerical simulation. This suggests that the collective coordinate approximation is a suitable method to investigate quasi-integrability in perturbed integrable models. We also discuss the general accuracy of this approximation by comparing our results with those of the full numerical simulations and find that the approximation is often remarkably accurate though less so when the models are a long way from the integrable case.

The numerical simulation of turbulence and flows in almost ideal, large-Reynolds-number astrophysical plasmas motivates the implementation of almost conservative MHD computer codes. They should efficiently calculate, use highly parallelized schemes scaling well with large numbers of CPU cores, allows to obtain a high grid resolution over large simulation domains and which can easily be adapted to new computer architectures as well as to new initial and boundary conditions, allow modular extensions. The new massively parallel simulation code GOEMHD3 enables efficient and fast simulations of almost ideal, large-Reynolds-number astrophysical plasma flows, well resolved and on huge grids covering large domains. Its abilities are validated by major tests of ideal and weakly dissipative plasma phenomena. The high resolution ($2048^3$ grid points) simulation of a large part of the solar corona above an observed active region proved the excellent parallel scalability of the code using more than 30.000 processor cores.

We show the numerical simulation result for the mass anomalous dimension of the SU($3$) gauge theory coupled to $N_f = 12$ fundamental fermions. We use two independent methods, namely the step scaling method and the hyperscaling method of the Dirac mode number, to determine the anomalous dimension in the vicinity of the infrared fixed point of the theory. We show the continuum extrapolations keeping the renormalized coupling constant as a reference in both analyses. Furthermore, some recent works seems to suggest the lower boundary of the conformal window of the SU($3$) gauge theory exists between $N_f=8$ and $10$. We also briefly report our new project, in which the numerical simulation of the SU($3$) gauge theory coupled to $N_f=9$ fundamental fermions has been performed.

We investigated the effects of gravitational lensing for a system in which a lens is a point mass and a homogeneous disc with a central hole. In such system there is a variety of cases resulting in formation of one, two and three Einstein rings. We found an explicit solution and considered conditions for existence of the second Einstein ring arising on the disc. Numerical modelling of the images was made for various ratios of the central mass to the disc one and for various values of the disc surface density. We also analysed dependence of the magnification factor on a source position for such system. The result of our work can be used in search of astrophysical objects with a toroidal (ring) structure.

We perform a full numerical simulation of binary spinning black holes to display the long term spin dynamics. We start the simulation at an initial proper separation between holes of d~25M and evolve them down to merger for nearly 48 orbits, 3 precession cycles and half of a flip-flop cycle. The simulation lasts for t=20000M and displays a change in the orientation of the spin of the secondary black hole from initially aligned with the orbital angular momentum to a complete anti-alignment after half of a flip-flop cycle. This process continuously flip-flops the spin during the lifetime of the binary. We discuss the consequences of this oscillation mode for accreting binaries, in particular for the spin growth and binary dynamics as well as the observational consequences for galactic and supermassive black holes.

We perform a full numerical simulation of binary spinning black holes to display the long term spin dynamics. We start the simulation at an initial proper separation between holes of d~25M and evolve them down to merger for nearly 48 orbits, 3 precession cycles and half of a flip-flop cycle. The simulation lasts for t=20000M and displays a change in the orientation of the spin of the secondary black hole from initially aligned with the orbital angular momentum to a complete anti-alignment after half of a flip-flop cycle. This process continuously flip-flops the spin during the lifetime of the binary. We discuss the consequences of this oscillation mode for accreting binaries, in particular for the spin growth and binary dynamics as well as the observational consequences for galactic and supermassive black holes.

We analyze the spiral structure that results in a numerical simulation of a galactic disk with stellar and gaseous components evolving in a potential that includes an axisymmetric halo and bulge. We perform a second simulation without the gas component to observe how it affects the spiral structure in the disk. To quantify this, we use a Fourier analysis and obtain values for the pitch angle and the velocity of the self-excited spiral pattern of the disk. The results show a tighter spiral in the simulation with gaseous component. The spiral structure is consistent with a superposition of waves, each with a constant pattern velocity in given radial ranges.

The burst of radio emission by the extensive air shower provides a promising alternative for detecting ultra-high energy cosmic rays.We have developed an independent numerical program to simulate these radio signals. Our code is based on a microscopic treatment, with both the geosynchrotron radiation and charge excess effect included. Here we make a first presentation of our basic program and its results. The time signal for different polarizations are computed, we find that the pulses take on a bipolar pattern, the spectrum is suppressed towards the lower frequencies.We investigate how the shower at different heights in atmosphere contribute to the total signal, and examine the signal strength and distribution at sites of different elevations. We also study the signal from showers of different inclination angles and azimuth directions. In all these cases we find the charge excess effect important.

We perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate holographic description of the thermalization of a strongly coupled plasma, which can model the dynamics of heavy ion collisions. The results indicate that previous calculations of the thermalization time may have been underestimates.

We perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate holographic description of the thermalization of a strongly coupled plasma, which can model the dynamics of heavy ion collisions. The results indicate that previous calculations of the thermalization time may have been underestimates.

We perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate holographic description of the thermalization of a strongly coupled plasma, which can model the dynamics of heavy ion collisions. The results indicate that previous calculations of the thermalization time may have been underestimates.

Superhalo electrons appear to be continuously present in the interplanetary medium, even at very quiet times, with a power-law spectrum at energies above $\sim$2 keV. Here we numerically investigate the generation of superhalo electrons by magnetic reconnection in the solar wind source region, using the MHD and test particle simulations for both single X-line reconnection and multiple X-line reconnection. We find that the direct current electric field, produced in the magnetic reconnection region, can accelerate electrons from an initial thermal energy of T $\sim10^5$ K up to hundreds of keV. After acceleration, some of the accelerated electrons, together with the nascent solar wind flow driven by the reconnection, propagate upwards along the newly-opened magnetic field lines into the interplanetary space, while the rest move downwards into the lower atmosphere. Similar to the observed superhalo electrons at 1 AU, the flux of the upward-traveling accelerated electrons versus energy displays a power-law distribution at $\sim$ 2 $-$ 100 keV, $f(E) \sim E^{-\delta}$, with a $\delta$ of $\sim$ 1.5 $-$ 2.4. For single (multiple) X-line reconnection, the spectrum becomes harder (softer) as the anomalous resistivity parameter $\alpha$ (uniform resistivity $\eta$) increases. These modeling results suggest that the acceleration in the solar wind source region may contribute to superhalo electrons.

A black hole accretion may have both the Keplerian and the sub-Keplerian components. We consider the most general accretion flow configuration, namely, two-component advective flow (TCAF) in which the Keplerian disk is immersed inside a low angular momentum, accreting sub-Keplerian halo component around a black hole. Low energy (soft) photons from the Keplerian component and hot electrons in the sub-Keplerian component exchange their energy through Comptonization or inverse-Comptonization processes. In the sub-Keplerian component, a shock is generally formed due to the centrifugal force. The post-shock region is known as the CENtrifugal pressure dominated BOundary Layer (CENBOL). The spectral and the timing properties of TCAF have been extensively studied using mostly analytical and some time dependent numerical simulations since the model was proposed by Chakrabarti & Titarchuk in 1995. The findings are the key inputs of understanding several observed features of black hole candidates. In this thesis, using numerical simulation, we rigorously prove some of the conjectures of the TCAF model. In the work presented in this thesis, we have considered for the first time the presence of both the Keplerian and the sub-Keplerian flow in a single simulation. The Keplerian disk resides on the equatorial plane and is the standard disk from which low energy photons having multi-color blackbody spectrum is emitted. The hydrodynamics as well as the thermal properties of the sub-Keplerian halo are simulated using a finite difference code which uses the principle of total variation diminishing (TVD). The Comptonization between the photons and the hot electrons is simulated using a Monte Carlo code. These two codes are then coupled and the resulting localized heating and cooling are included in the coupled code. Using this code, we study the spectral and timing properties of the TCAF.

We study the formation of coronal jets through numerical simulation of the emergence of a twisted magnetic flux rope into a pre-existing open magnetic field. Reconnection inside the emerging flux rope in addition to that between the emerging and pre-existing fields give rise to the violent eruption studied. The simulated event closely resembles the coronal jets ubiquitously observed by Hinode/XRT and demonstrates that heated plasma is driven into the extended atmosphere above. Thermal conduction implemented in the model allows us to qualitatively compare simulated and observed emission from such events. We find that untwisting field lines after the reconnection drive spinning outflows of plasma in the jet column. The Poynting flux in the simulated jet is dominated by the untwisting motions of the magnetic fields loaded with high-density plasma. The simulated jet is comprised of spires of untwisting field that are loaded with a mixture of cold and hot plasma and exhibit rotational motion of order 20 km/s and match contemporary observations.

We perform and extend real-time numerical simulation of a low-dimensional scalar field theory or a quantum mechanical system using stochastic quantization. After a brief review of the quantization method and the complex Langevin dynamics, we calculate the propagator and make a comparison with analytical results. This is a first step toward general applications, and we focus only on the vacuum properties of the theory; this enables us to handle the boundary condition with the $i\epsilon$ prescription in frequency space. While we can control stability of the numerical simulation for any coupling strength, our results turn out to flow into an unphysical fixed-point, which is qualitatively understood from the corresponding Fokker-Planck equation. We propose a simple truncation scheme, "restricted phase-space approximation," to avoid the unphysical fixed-point. With this method, we obtain stable results at reasonably good accuracy. Finally we give a short discussion on the closed-time path formalism and demonstrate the direct computation of the vacuum expectation value not with the $i\epsilon$ prescription but from an explicit construction of the Feynman kernel.

We perform and extend real-time numerical simulation of a low-dimensional scalar field theory or a quantum mechanical system using stochastic quantization. After a brief review of the quantization method and the complex Langevin dynamics, we calculate the propagator and make a comparison with analytical results. This is a first step toward general applications, and we focus only on the vacuum properties of the theory; this enables us to handle the boundary condition with the $i\epsilon$ prescription in frequency space. While we can control stability of the numerical simulation for any coupling strength, our results turn out to flow into an unphysical fixed-point, which is qualitatively understood from the corresponding Fokker-Planck equation. We propose a simple truncation scheme, "restricted phase-space approximation," to avoid the unphysical fixed-point. With this method, we obtain stable results at reasonably good accuracy. Finally we give a short discussion on the closed-time path formalism and demonstrate the direct computation of the vacuum expectation value not with the $i\epsilon$ prescription but from an explicit construction of the Feynman kernel.

We perform and extend real-time numerical simulation of a scalar quantum field theory using stochastic quantization. After a brief review of the quantization method, we calculate the propagator and the perturbative series and compare with analytical results. This is a first step toward general applications, and we focus only on the vacuum properties of the theory; this enables us to handle the boundary condition by the $i\epsilon$ prescription. Then, we explicitly check the convergence and solve the differential equation in frequency space. For clarity we drop the spatial-derivative terms and make a comparison between our results and the numerically exact results obtained by diagonalization of the Hamiltonian. While we can control stability of the numerical simulation for any coupling strength, our results turn out to flow into an unphysical attractor if the simulation is out of the weak-coupling regime. We propose a simple truncation scheme to incorporate the interaction terms, which we name the "restricted phase-space approximation." With this method, we obtain results with stable simulation at good accuracy. Finally we give a short discussion on the closed-time path formalism.

We perform and extend real-time numerical simulation of a scalar quantum field theory using stochastic quantization. After a brief review of the quantization method, we calculate the propagator and the perturbative series and compare with analytical results. This is a first step toward general applications, and we focus only on the vacuum properties of the theory; this enables us to handle the boundary condition by the $i\epsilon$ prescription. Then, we explicitly check the convergence and solve the differential equation in frequency space. For clarity we drop the spatial-derivative terms and make a comparison between our results and the numerically exact results obtained by diagonalization of the Hamiltonian. While we can control stability of the numerical simulation for any coupling strength, our results turn out to flow into an unphysical attractor if the simulation is out of the weak-coupling regime. We propose a simple truncation scheme to incorporate the interaction terms, which we name the "restricted phase-space approximation." With this method, we obtain results with stable simulation at good accuracy. Finally we give a short discussion on the closed-time path formalism.

We present our prediction for the local 21 cm differential brightness temperature ($\delta T_{b}$) from a set of strongly clustered sources of Population III (Pop III) and II (Pop II) objects in the early Universe, by a numerical simulation of their formation and radiative feedback. These objects are located inside a highly biased environment, which is a rare, high-density peak ("Rarepeak") extending to $\sim7$ comoving Mpc. We study the impact of ultraviolet (UV) and X-ray photons on the intergalactic medium (IGM) and the resulting $\delta T_{b}$, when Pop III stars are assumed to emit X-ray photons by forming X-ray binaries very efficiently. We parameterize the rest-frame spectral energy distribution (SED) of X-ray photons, which regulates X-ray photon-trapping, IGM-heating, secondary Lyman-alpha pumping and the resulting morphology of $\delta T_{b}$. A combination of emission ($\delta T_{b}>0$) and absorption ($\delta T_{b}<0$) regions appears in varying amplitudes and angular scales. The boost of the signal by the high-density environment ($\delta\sim0.64$) and on a relatively large scale combine to make Rarepeak a discernible, spatially-extended ($\theta\sim10′$) object for 21 cm observation at $13\lesssim z\lesssim17$, which is found to be detectable as a single object by SKA with integration time of $\sim1000$ hours. Power spectrum analysis by some of the SKA precursors (LOFAR, MWA, PAPER) of such rare peaks is found difficult due to the rarity of these peaks, and the contribution only by these rare peaks to the total power spectrum remains subdominant compared to that by all astrophysical sources.

The strong-field region inside a black hole needs special attention during numerical simulation. One approach for handling the problem is the moving puncture method, which has become an important tool in numerical relativity since it allows long term simulations of binary black holes. An essential component of this method is the choice of the ’1+log’-slicing condition. We present an investigation of this slicing condition in rotating black hole spacetimes. We discuss how the results of the stationary Schwarzschild ’1+log’-trumpet change when spin is added. This modification enables a simple and cheap algorithm for determining the spin of a non-moving black hole for this particular slicing condition. Applicability of the algorithm is verified in simulations of single black hole, binary neutron star and mixed binary simulations.

We present a comparison of the Solar Dynamics Observatory (SDO) analysis of NOAA Active Region (AR) 11158 and numerical simulations of flux-tube emergence, aiming to investigate the formation process of this flare-productive AR. First, we use SDO/Helioseismic and Magnetic Imager (HMI) magnetograms to investigate the photospheric evolution and Atmospheric Imaging Assembly (AIA) data to analyze the relevant coronal structures. Key features of this quadrupolar region are a long sheared polarity inversion line (PIL) in the central delta-sunspots and a coronal arcade above the PIL. We find that these features are responsible for the production of intense flares, including an X2.2-class event. Based on the observations, we then propose two possible models for the creation of AR 11158 and conduct flux-emergence simulations of the two cases to reproduce this AR. Case 1 is the emergence of a single flux tube, which is split into two in the convection zone and emerges at two locations, while Case 2 is the emergence of two isolated but neighboring tubes. We find that, in Case 1, a sheared PIL and a coronal arcade are created in the middle of the region, which agrees with the AR 11158 observation. However, Case 2 never builds a clear PIL, which deviates from the observation. Therefore, we conclude that the flare-productive AR 11158 is, between the two cases, more likely to be created from a single split emerging flux than from two independent flux bundles.

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation, we compute the probability distribution of curvature fluctuations, paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter space.

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation, we compute the probability distribution of curvature fluctuations, paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter space.

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation, we compute the probability distribution of curvature fluctuations, paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter space.

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation we compute the probability distribution of curvature fluctuations paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter-space.

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation we compute the probability distribution of curvature fluctuations paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter-space.

We study the production of primordial black holes (PBHs) during the preheating stage that follows a chaotic inflationary phase. The scalar fields present in the process are evolved numerically using a modified version of the HLATTICE code. From the output of the numerical simulation we compute the probability distribution of curvature fluctuations paying particular attention to sub-horizon scales. We find that in some specific models these modes grow to large amplitudes developing highly non-Gaussian probability distributions. We then calculate PBH abundances using the standard Press-Schechter criterion and find that overproduction of PBHs is likely in some regions of the chaotic preheating parameter-space.

We present a model of the magnetosphere around an oscillating neutron star. The electromagnetic fields are numerically solved by modeling electric charge and current induced by the stellar torsional mode, with particular emphasis on outgoing radiation passing through the magnetosphere. The current is modeled using Ohm’s law, whereby an increase in conductivity results in an increase in the induced current. As a result, the fields are drastically modified, and energy flux is thereby enhanced. This behavior is however localized in the vicinity of the surface since the induced current disappears outwardly in our model, in which the exterior is assumed to gradually approach a vacuum.

Interpreting the nature of starless cores has been a prominent goal in star formation for many years. In order to characterise the evolutionary stages of these objects, we perform synthetic observations of a numerical simulation of a turbulent molecular cloud. We find that nearly all cores that we detect are associated with filaments and eventually form protostars. We conclude that observed starless cores which appear Jeans unstable are only marginally larger than their respective Jeans masses (within a factor of 3). We note single dish observations such as those performed with the JCMT appear to miss significant core structure on small scales due to beam averaging. Finally, we predict that interferometric observations with ALMA Cycle 1 will resolve the important small scale structure, which has so far been missed by mm-wavelength observations.

Interpreting the nature of starless cores has been a prominent goal in star formation for many years. In order to characterise the evolutionary stages of these objects, we perform synthetic observations of a numerical simulation of a turbulent molecular cloud. We find that nearly all cores that we detect are associated with filaments and eventually form protostars. We conclude that observed starless cores which appear Jeans unstable are only marginally larger than their respective Jeans masses (within a factor of 3). We note single dish observations such as those performed with the JCMT appear to miss significant core structure on small scales due to beam averaging. Finally, we predict that interferometric observations with ALMA Cycle 1 will resolve the important small scale structure, which has so far been missed by mm-wavelength observations.

Three-dimensional (3D), time dependent numerical simulations, of flow of matter in stars, now have sufficient resolution to be fully turbulent. The late stages of the evolution of massive stars, leading up to core collapse to a neutron star (or black hole), and often to supernova explosion and nucleosynthesis, are strongly convective because of vigorous neutrino cooling and nuclear heating. Unlike models based on current stellar evolutionary practice, these simulations show a chaotic dynamics characteristic of highly turbulent flow. Theoretical analysis of this flow, both in the Reynolds-averaged Navier-Stokes (RANS) framework and by simple dynamic models, show an encouraging consistency with the numerical results. It may now be possible to develop physically realistic and robust procedures for convection and mixing which (unlike 3D numerical simulation) may be applied throughout the long life times of stars. In addition, a new picture of the presupernova stages is emerging which is more dynamic and interesting (i.e., predictive of new and newly observed phenomena) than our previous one.

Three-dimensional (3D), time dependent numerical simulations, of flow of matter in stars, now have sufficient resolution to be fully turbulent. The late stages of the evolution of massive stars, leading up to core collapse to a neutron star (or black hole), and often to supernova explosion and nucleosynthesis, are strongly convective because of vigorous neutrino cooling and nuclear heating. Unlike models based on current stellar evolutionary practice, these simulations show a chaotic dynamics characteristic of highly turbulent flow. Theoretical analysis of this flow, both in the Reynolds-averaged Navier-Stokes (RANS) framework and by simple dynamic models, show an encouraging consistency with the numerical results. It may now be possible to develop physically realistic and robust procedures for convection and mixing which (unlike 3D numerical simulation) may be applied throughout the long life times of stars. In addition, a new picture of the presupernova stages is emerging which is more dynamic and interesting (i.e., predictive of new and newly observed phenomena) than our previous one.

In a superhigh magnetic field, direct Urca reactions can proceed for an arbitrary proton concentration. Since only the electrons with high energy $E$ ($E > Q$, $Q$ is the threshold energy of inverse $\beta-$decay) at large Landau levels can be captured, we introduce the Landau level effect coefficient $q$ and the effective electron capture rate $\Gamma_{\rm eff}$. By using $\Gamma_{\rm eff}$, the values of $L_{\rm X}$ and $L_{\rm \nu}$ are calculated, where and $L_{\rm \nu}$, $L_{\rm X}$ are the average neutrino luminosity of Anomalous X-ray Pulsars (AXPs) and the average X-ray luminosity of AXPs, respectively. The complete process of electron capture inside a magnetar is simulated numerically.

We present an extension to multiple planes of the gravitational lensing code {\small GLAMER}. The method entails projecting the mass in the observed light-cone onto a discrete number of lens planes and inverse ray-shooting from the image to the source plane. The mass on each plane can be represented as halos, simulation particles, a projected mass map extracted form a numerical simulation or any combination of these. The image finding is done in a source oriented fashion, where only regions of interest are iteratively refined on an initially coarse image plane grid. The calculations are performed in parallel on shared memory machines. The code is able to handle different types of analytic halos (NFW, NSIE, power-law, etc.), haloes extracted from numerical simulations and clusters constructed from semi-analytic models ({\small MOKA}). Likewise, there are several different options for modeling the source(s) which can be distributed throughout the light-cone. The distribution of matter in the light-cone can be either taken from a pre-existing N-body numerical simulations, from halo catalogs, or are generated from an analytic mass function. We present several tests of the code and demonstrate some of its applications such as generating mock images of galaxy and galaxy cluster lenses.

Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall present the nonlinear results for cosmic ray transport, in particular, the cross field transport of CRs and demonstrate that the concept of cosmic ray subdiffusion in general does not apply and the perpendicular motion is well described by normal diffusion with M_A^4 dependence. Moreover, on scales less than injection scale of turbulence, CRs’ transport becomes super-diffusive. Quantitative predictions for both the normal diffusion on large scale and super diffusion are confronted with recent numerical simulations. Implication for shock acceleration is briefly discussed.

Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall present the nonlinear results for cosmic ray transport, in particular, the cross field transport of CRs and demonstrate that the concept of cosmic ray subdiffusion in general does not apply and the perpendicular motion is well described by normal diffusion with M_A^4 dependence. Moreover, on scales less than injection scale of turbulence, CRs’ transport becomes super-diffusive. Quantitative predictions for both the normal diffusion on large scale and super diffusion are confronted with recent numerical simulations. Implication for shock acceleration is briefly discussed.

We study the spectral and timing properties of a two component advective flow (TCAF) around a black hole by numerical simulation. Several cases have been simulated by varying the Keplerian disk rate and the resulting spectra and lightcurves have been produced for all the cases. The dependence of the spectral states and quasi-periodic oscillation (QPO) frequencies on the flow parameters is discussed. We also find the earlier explanation of arising of QPOs as the resonance between infall time scale and cooling time scale remain valid even for Compton cooling.

In this paper a new scalable hydrodynamic code GPUPEGAS (GPU-accelerated PErformance Gas Astrophysic Simulation) for simulation of interacting galaxies is proposed. The code is based on combination of Godunov method as well as on the original implementation of FlIC method, specially adapted for GPU-implementation. Fast Fourier Transform is used for Poisson equation solution in GPUPEGAS. Software implementation of the above methods was tested on classical gas dynamics problems, new Aksenov’s test and classical gravitational gas dynamics problems. Collisionless hydrodynamic approach was used for modelling of stars and dark matter. The scalability of GPUPEGAS computational accelerators is shown.

Motivated by the problem of local solar subsurface magnetic structure, we have used numerical simulation to investigate the propagation of waves through monolithic magnetic flux tubes of different size. A cluster model can be a good approximation to simulate sunspots as well as solar plage regions which are composed of an ensemble of compactly packed thin flux tubes. Simulations of this type is a powerful tool to probe the structure and the dynamic of various solar features which are related directly to solar magnetic field activity.

Results of numerical simulation constructed before strict mathematical model of an establishment of thermodynamic equilibrium in originally nonequilibrium cosmological ultrarelativistic plasma for the Universe with any acceleration in the assumption of restoration of a scalling of interactions of elementary particles are presented at energies above a unitary limit. Limiting parametres of residual nonequilibrium distribution of nonequilibrium relic particles of ultrahigh energies are found.

Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate discretization is crucial. Adaptive grids with cuboidal cells such as octrees have proven very popular, however several recently introduced hydrodynamical and RT codes are based on a Voronoi tessellation of the spatial domain. Such an unstructured grid poses new challenges in laying down the rays (straight paths) needed in RT codes. We show that it is straightforward to implement accurate and efficient RT on 3D Voronoi grids. We present a method for computing straight paths between two arbitrary points through a 3D Voronoi grid in the context of a RT code. We implement such a grid in our RT code SKIRT, using the open source library Voro++ to obtain the relevant properties of the Voronoi grid cells based solely on the generating points. We compare the results obtained through the Voronoi grid with those generated by an octree grid for two synthetic models, and we perform the well-known Pascucci RT benchmark using the Voronoi grid. The presented algorithm produces correct results for our test models. Shooting photon packages through the geometrically much more complex 3D Voronoi grid is only about three times slower than the equivalent process in an octree grid with the same number of cells, while in fact the total number of Voronoi grid cells may be lower for an equally good representation of the density field. We conclude that the benefits of using a Voronoi grid in RT simulation codes will often outweigh the somewhat slower performance.

We report on the filaments that develop self-consistently in a new numerical simulation of cloud formation by colliding flows. As in previous studies, the forming cloud begins to undergo gravitational collapse because it rapidly acquires a mass much larger than the average Jeans mass. Thus, the collapse soon becomes nearly pressureless, proceeding along its shortest dimension first. This naturally produces filaments in the cloud, and clumps within the filaments. The filaments are not in equilibrium at any time, but instead are long-lived flow features, through which the gas flows from the cloud to the clumps. The filaments are long-lived because they accrete from their environment while simultaneously accreting onto the clumps within them; they are essentially the locus where the flow changes from accreting in two dimensions to accreting in one dimension. Moreover, the clumps also exhibit a hierarchical nature: the gas in a filament flows onto a main, central clump, but other, smaller-scale clumps form along the infalling gas. Correspondingly, the velocity along the filament exhibits a hierarchy of jumps at the locations of the clumps. Two prominent filaments in the simulation have lengths ~15 pc, and masses ~600 Msun above density n ~ 10^3 cm-3 (~2×10^3 Msun at n > 50 cm-3). The density profile exhibits a central flattened core of size ~0.3 pc and an envelope that decays as r^-2.5, in reasonable agreement with observations. Accretion onto the filament reaches a maximum linear density rate of ~30 Msun Myr^-1 pc^-1.

We report on the filaments that develop self-consistently in a new numerical simulation of cloud formation by colliding flows. As in previous studies, the forming cloud begins to undergo gravitational collapse because it rapidly acquires a mass much larger than the average Jeans mass. Thus, the collapse soon becomes nearly pressureless, proceeding along its shortest dimension first. This naturally produces filaments in the cloud, and clumps within the filaments. The filaments are not in equilibrium at any time, but instead are long-lived flow features, through which the gas flows from the cloud to the clumps. The filaments are long-lived because they accrete from their environment while simultaneously accreting onto the clumps within them; they are essentially the locus where the flow changes from accreting in two dimensions to accreting in one dimension. Moreover, the clumps also exhibit a hierarchical nature: the gas in a filament flows onto a main, central clump, but other, smaller-scale clumps form along the infalling gas. Correspondingly, the velocity along the filament exhibits a hierarchy of jumps at the locations of the clumps. Two prominent filaments in the simulation have lengths ~15 pc, and masses ~600 Msun above density n ~ 10^3 cm-3 (~2×10^3 Msun at n > 50 cm-3). The density profile exhibits a central flattened core of size ~0.3 pc and an envelope that decays as r^-2.5, in reasonable agreement with observations. Accretion onto the filament reaches a maximum linear density rate of ~30 Msun Myr^-1 pc^-1.

We report on the filaments that develop self-consistently in a new numerical simulation of cloud formation by colliding flows. As in previous studies, the forming cloud begins to undergo gravitational collapse because it rapidly acquires a mass much larger than the average Jeans mass. Thus, the collapse soon becomes nearly pressureless, proceeding along its shortest dimension first. This naturally produces filaments in the cloud, and clumps within the filaments. The filaments are not in equilibrium at any time, but instead are long-lived flow features, through which the gas flows from the cloud to the clumps. The filaments are long-lived because they accrete from their environment while simultaneously accreting onto the clumps within them; they are essentially the locus where the flow changes from accreting in two dimensions to accreting in one dimension. Moreover, the clumps also exhibit a hierarchical nature: the gas in a filament flows onto a main, central clump, but other, smaller-scale clumps form along the infalling gas. Correspondingly, the velocity along the filament exhibits a hierarchy of jumps at the locations of the clumps. Two prominent filaments in the simulation have lengths ~15 pc, and masses ~600 Msun above density n ~ 10^3 cm-3 (~2×10^3 Msun at n > 50 cm-3). The density profile exhibits a central flattened core of size ~0.3 pc and an envelope that decays as r^-2.5, in reasonable agreement with observations. Accretion onto the filament reaches a maximum linear density rate of ~30 Msun Myr^-1 pc^-1.

Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through use of integer spin weighted spherical harmonics we present a method which allows for the implementation of arbitrary tensorial evolution equations. Our method combines two numerical techniques that were originally developed with different applications in mind. The first is Huffenberger and Wandelt’s spectral decomposition algorithm to perform the mapping from physical to spectral space. The second is the application of Luscombe and Luban’s method, to convert numerically divergent linear recursions into stable nonlinear recursions, to the calculation of reduced Wigner d-functions. We give a detailed discussion of the theory and numerical implementation of our algorithm. The properties of our method are investigated by solving the scalar and vectorial advection equation on the sphere, as well as the 2+1 Maxwell equations on a deformed sphere.